Off-line Admission Control for Advance Reservations in Star Networks

  • Udo Adamy
  • Thomas Erlebach
  • Dieter Mitsche
  • Ingo Schurr
  • Bettina Speckmann
  • Emo Welzl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3351)


Given a network together with a set of connection requests, call admission control is the problem of deciding which calls to accept and which ones to reject in order to maximize the total profit of the accepted requests. We consider call admission control problems with advance reservations in star networks. For the most general variant we present a constant-factor approximation algorithm resolving an open problem due to Erlebach. Our method is randomized and achieves an approximation ratio of 1/18. It can be generalized to accommodate call alternatives, in which case the approximation ratio is 1/24. We show how our method can be derandomized. In addition we prove that call admission control in star networks is \({\mathcal APX}\)-hard even for very restricted variants of the problem.


Admission Control Approximation Ratio Connection Request Call Admission Control Advance Reservation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. Wiley, New York (1992)zbMATHGoogle Scholar
  2. 2.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin (1999)zbMATHGoogle Scholar
  3. 3.
    Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J.S., Schieber, B.: A unified approach to approximating resource allocation and scheduling. Journal of the ACM (JACM) 48(5), 1069–1090 (2001)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics 25, 27–46 (1985)MathSciNetGoogle Scholar
  5. 5.
    Berman, P., DasGupta, B., Muthukrishnan, S., Ramaswami, S.: Improved approximation algorithms for rectangle tiling and packing. In: Proceedings of the 12th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA), pp. 427–436 (2001)Google Scholar
  6. 6.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  7. 7.
    Chakrabarti, A., Chekuri, C., Gupta, A., Kumar, A.: Approximation algorithms for the unsplittable flow problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 51–66. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Chekuri, C., Mydlarz, M., Shepherd, F.B.: Multicommodity demand flow in a tree. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 410–425. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Duffield, N.G., Goyal, P., Greenberg, A., Mishra, P., Ramakrishnan, K.K., van der Merwe, J.E.: Resource management with hoses: point-to-cloud services for virtual private networks. IEEE/ACM Transactions on Networking (TON) 10(5), 679–692 (2002)CrossRefGoogle Scholar
  10. 10.
    Edmonds, J.: Paths, trees and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    T. Erlebach. Call admission control for advance reservation requests with alternatives. In Proceedings of the 3rd Workshop on Approximation and Randomization Algorithms in Communication Networks (ARACNE), Proceedings in Informatics, pages 51–64. Carleton Scientific, 2002.Google Scholar
  12. 12.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  13. 13.
    Guérin, R.A., Orda, A.: Networks with advance reservations: The routing perspective. In: Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pp. 118–127. IEEE Computer Society Press, Los Alamitos (2000)Google Scholar
  14. 14.
    Guruswami, V., Khanna, S., Rajaraman, R., Shepherd, B., Yannakakis, M.: Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 19–28 (1999)Google Scholar
  15. 15.
    Kann, V.: Maximum bounded 3-dimensional matching is MAX SNP-complete. Information Processing Letters 37, 27–35 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kleinberg, J.: Approximation algorithms for disjoint paths problems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (1996)Google Scholar
  17. 17.
    Leonardi, S.: On-line network routing. In: Fiat, A., Woeginger, G.J. (eds.) Dagstuhl Seminar 1996. LNCS, vol. 1442, Springer, Berlin (1998)Google Scholar
  18. 18.
    Lewin-Eytan, L., Naor, J.S., Orda, A.: Routing and admission control in networks with advance reservations. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 215–228. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Micali, S., Vazirani, V.V.: An O(\(\sqrt{|V|}\cdot|E|\)) algorithm for finding maximum matchings in general graphs. In: Proceedings of the 21st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 17–27 (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Udo Adamy
    • 1
  • Thomas Erlebach
    • 2
  • Dieter Mitsche
    • 1
  • Ingo Schurr
    • 1
  • Bettina Speckmann
    • 3
  • Emo Welzl
    • 1
  1. 1.Institute for Theoretical Computer ScienceETH ZürichZürichSwitzerland
  2. 2.Department of Computer ScienceUniversity of LeicesterLeicesterUK
  3. 3.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands

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